Question

Interactive LearningWare 16.2 provides some pertinent background for this problem. A convertible moves toward you and then passes you; all the while, its loudspeakers are producing a sound. The speed of the car is a constant 5.73 m/s, and the speed of sound is 343 m/s. What is the ratio of the frequency you hear while the car is approaching to the frequency you hear while the car is moving away?

Answer 1

The ratio is 1.03

Step-by-step explanation:

The ratio of the frequency that is heard while the car is approaching
`f_(ap)` to the frequency that is heard while the car is moving away
`f_(ma)` can be calculated using the Doppler effect equation:

`(f_(ap))/(f_(ma)) = \frac {f_(0) (v_(s) - v_(r))/(v_(s) - v_(e))}{f_(0) (v_(s) - v_(r))/(v_(s) + v_(e))}`

where
`f_(o)`: is the emitted frequency,
`v_(s)`: is the speed of sound,
`v_(r)`: is the speed of the receptor and
`v_(c)`: is the emissor speed

`(f_(ap))/(f_(ma)) = (v_(s) + v_(e))/(v_(s) - v_(e)) = (343 + 5.73)/(343 - 5.73) = 1.03`

Therefore the ratio is 1.03.

I hope it helps you!